Regional Stability Analysis of Transitional Fluid Flows

Leonardo F. Toso, Ross Drummond, Stephen R. Duncan

Abstract: A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model’s nonlinearities are both lossless and locally bounded and uses the axes lengths of the ellipsoids for the trajectory set containment as variables in the stability conditions. Compared to existing approaches based on quadratic constraints, the proposed method leads to an average increase in the maximum allowable energy perturbation of ≈ 29% for the 4-state Waleffe-Kim-Hamilton (WKH) shear flow model and of ≈ 38% for the 9-state reduced model of Couette flow.